Because the derivative of a function y
) is itself a function y′
), you can take the derivative of f′
), which is generally referred to as the second derivative of f(x)
and written f“
) or f 2
). This differentiation process can be continued to find the third, fourth, and successive derivatives of f
), which are called higher order derivatives
). Because the “prime” notation for derivatives would eventually become somewhat messy, it is preferable to use the numerical notation f
) = y
) to denote the n
th derivative of f
Example 1: Find the first, second, and third derivatives of f( x) = 5 x 4 − 3x 3 + 7x 2 − 9x + 2.
Example 2: Find the first, second, and third derivatives of y = sin 2 x.
Example 3: Find f (3) (4) if .